Question 1176893
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    x + 3x + (2x+4) = 54


        6x =        = 54 - 4 = 50


         x                   = {{{50/6}}} = 8 {{{1/3}}}  inches.


The sides are  x = 8 {{{1/3}}}  inches (shortest);  3x = 25 inches ("one side")  and  (2x+4) = 20 {{{2/3}}}  inches  ("the third side").


As always, when you solve such problems, you must check at the end if the triangle inequalities 
are held (to check if a triangle with such sides does really exist).



In this case, the triangle inequalities are valid, so such a triangle does exist.
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Solved.